mad
Median Absolute Deviation
Compute the median absolute deviation, i.e., the (lo-/hi-) median of the absolute deviations from the median, and (by default) adjust by a factor for asymptotically normal consistency.
Usage
mad(x, center = median(x), constant = 1.4826, na.rm = FALSE,
low = FALSE, high = FALSE)Arguments
- x
a numeric vector.
- center
Optionally, the centre: defaults to the median.
- constant
scale factor.
- na.rm
if
TRUEthenNAvalues are stripped fromxbefore computation takes place.- low
if
TRUE, compute the ‘lo-median’, i.e., for even sample size, do not average the two middle values, but take the smaller one.- high
if
TRUE, compute the ‘hi-median’, i.e., take the larger of the two middle values for even sample size.
Details
The actual value calculated is constant * cMedian(abs(x - center))
with the default value of center being median(x), and
cMedian being the usual, the ‘low’ or ‘high’ median, see
the arguments description for low and high above.
The default constant = 1.4826 (approximately
\(1/\Phi^{-1}(\frac 3 4)\) = 1/qnorm(3/4))
ensures consistency, i.e.,
$$E[mad(X_1,\dots,X_n)] = \sigma$$
for \(X_i\) distributed as \(N(\mu, \sigma^2)\)
and large \(n\).
If na.rm is TRUE then NA
values are stripped from x before computation takes place.
If this is not done then an NA value in
x will cause mad to return NA.
See Also
Examples
library(stats)
# NOT RUN {
mad(c(1:9))
print(mad(c(1:9), constant = 1)) ==
mad(c(1:8, 100), constant = 1) # = 2 ; TRUE
x <- c(1,2,3,5,7,8)
sort(abs(x - median(x)))
c(mad(x, constant = 1),
mad(x, constant = 1, low = TRUE),
mad(x, constant = 1, high = TRUE))
# }